the_fingerprint_of_god.py
God's or any other Supreme Entity's attributes can be directly connected with Fibonacci Series and its golden ratio.
What is Fibonacci Series?
The Fibonacci Series is named after Leonardo Pisano (also known as Fibonacci ), an Italian mathematician who lived from 1170 – 1250.
In short, the pattern is 0,1,1,2,3,5,8,13… and so on to infinity. The sequence is always adding the last two numbers to get the next number(0+1=1, 1+1=2, 1+2=3, 2+3=5....)
Golden Ratio:
Starting with fifth member in the Fibonacci series, 5/3=8/5=13/8~1.6
The golden ratio is roughly 1.618, or its inverse 0.618. This proportion is known by many names: the golden ratio, the golden mean, PHI, and the divine proportion, among others. So, why is this number so important? The Golden Ratio describes proportions of everything from atoms to huge stars in the sky. Nature uses this ratio to maintain balance.
Don't believe it? Take honeybees, for example. If you divide the female bees by the male bees in any given hive, you will get 1.618. Sunflowers, which have opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation. This same ratio can be seen in relationships between different components throughout nature.
Are you still having trouble believing it? Try measuring from your shoulder to your fingertips, and then divide this number by the length from your elbow to your fingertips. Or try measuring from your head to your feet, and divide that by the length from your belly button to your feet. Are the results the same? Somewhere in the area of 1.618? The golden ratio is seemingly unavoidable.
Golden rectangle
A golden rectangle is a rectangle whose side lengths are in the golden ratio,The rectangle is 3 by 5, which happens to be two of the integers in the Fibonacci numbers. The “golden ratio” is in sync with the Fibonacci pattern
Golden spiral:
A golden spiral is a logarithmic spiral whose growth factor is φ(phi), the golden ratio. That is, a golden spiral gets wider (or further from its origin) by a factor of φ for every quarter turn it makes.
While the Golden Ratio doesn't account for every structure or pattern in the universe, it's certainly a major player. Here are some examples.
1.Flower petals
The number of petals in a flower consistently follows the Fibonacci sequence. Famous examples include the lily, which has three petals, buttercups, which have five , the chicory's 21, the daisy's 34, and so on. Phi appears in petals on account of the ideal packing arrangement as selected by Darwinian processes; each petal is placed at 0.618034 per turn (out of a 360° circle) allowing for the best possible exposure to sunlight and other factors.
2.Seed Head
The head of a flower is also subject to Fibonaccian processes. Typically, seeds are produced at the center, and then migrate towards the outside to fill all the space. Sunflowers provide a great example of these spiraling patterns.
In some cases, the seed heads are so tightly packed that total number can get quite high — as many as 144 or more. And when counting these spirals, the total tends to match a Fibonacci number. Interestingly, a highly irrational number is required to optimize filling (namely one that will not be well represented by a fraction). Phi fits the bill rather nicely.
3. Pinecones
Similarly, the seed pods on a pinecone are arranged in a spiral pattern. Each cone consists of a pair of spirals, each one spiraling upwards in opposing directions. The number of steps will almost always match a pair of consecutive Fibonacci numbers. For example, a 3-5 cone is a cone which meets at the back after three steps along the left spiral, and five steps along the right.
4. Fruits and Vegetables
Likewise, similar spiraling patterns can be found on pineapples and cauliflower
5. Tree branches
The Fibonacci sequence can also be seen in the way tree branches form or split. A main trunk will grow until it produces a branch, which creates two growth points. Then, one of the new stems branches into two, while the other one lies dormant. This pattern of branching is repeated for each of the new stems. A good example is the sneezewort. Root systems and even algae exhibit this pattern.
6. Shells
The unique properties of the Golden Rectangle provides another example. This shape, a rectangle in which the ratio of the sides a/b is equal to the golden mean (phi), can result in a nesting process that can be repeated into infinity — and which takes on the form of a spiral. It's call the logarithmic spiral, and it abounds in nature.
Snail shells and nautilus shells follow the logarithmic spiral, as does the cochlea of the inner ear. It can also be seen in the horns of certain goats, and the shape of certain spider's webs
7. Spiral Galaxies
Not surprisingly, spiral galaxies also follow the familiar Fibonacci pattern. The Milky Way has several spiral arms, each of them a logarithmic spiral of about 12 degrees.
8. Hurricanes
9. Faces
Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can been seen from the side, and even the eye and ear itself (which follows along a spiral).
It's worth noting that every person's body is different, but that averages across populations tend towards phi. It has also been said that the more closely our proportions adhere to phi, the more "attractive" those traits are perceived.
10. Fingers and hands
Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the ratio of phi.
11. Animal bodies
Animal bodies exhibit similar tendencies, including dolphins (the eye, fins and tail all fall at Golden Sections), starfish, sand dollars, sea urchins, ants, and honey bees.
12. Reproductive dynamics
Speaking of honey bees, they follow Fibonacci in other interesting ways. The most profound example is by dividing the number of females in a colony by the number of males (females always outnumber males). The answer is typically something very close to 1.618. In addition, the family tree of honey bees also follows the familiar pattern. Males have one parent (a female), whereas females have two (a female and male). Thus, when it comes to the family tree, males have 2, 3, 5, and 8 grandparents, great-grandparents, gr-gr-grandparents, and gr-gr-gr-grandparents respectively. Following the same pattern, females have 2, 3, 5, 8, 13, and so on. And as noted, bee physiology also follows along the Golden Curve rather nicely.
13. Animal fight patterns
When a hawk approaches its prey, its sharpest view is at an angle to their direction of flight — an angle that's the same as the spiral's pitch.
14. The uterus
According to a study, that measured over 5,000 women using ultrasound to draw the average ratio of a uterus's length to its width for different age bands.
The data shows that this ratio is about 2 at birth and then it steadily decreases through a woman's life to 1.46 when she is in old age.
Most interesting fact is women are at their most fertile, between the ages of 16 and 20, the ratio of length to width of a uterus is 1.6 – a very good approximation to the golden ratio.
15. DNA molecules
Even the microscopic realm is not immune to Fibonacci. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.
Python Program to generate Fibonacci Series:
1.Using Loops
#Using Loops:
a=int(input("Enter the terms: "))
f=0 #first element of series
s=1 #second element of series
if a<=0:
print("The requested series is",f)
else:
print(f,s,end=" ")
for x in range(2,a):
next=f+s
print(next,end=" ")
f=s
s=next
Output:
Enter the terms: 7
0 1 1 2 3 5 8
2.Using Recursion
#Using Recursion:
def recur_fibo(n):
if n <= 1:
return n
else:
return(recur_fibo(n-1) + recur_fibo(n-2))
# take input from the user
nterms = int(input("How many terms? "))
# check if the number of terms is valid
if nterms <= 0:
print("Plese enter a positive integer")
else:
print("Fibonacci sequence:")
for i in range(nterms):
print(recur_fibo(i))
Output:
How many terms? 7
Fibonacci sequence:
0
1
1
2
3
5
8